The Kokutetsu era refers to the period 1949-1987 when Japan National Railways (abbreviated to JNR or Kokutetsu) was operating. The Sakurajima-Takachiho Express service ran between Tokyo station and Nishi-Kagoshima station. Depending on the exact route, the scheduled time taken would be as short as 25 hours 33 minutes or up to 28 hours 20 minutes.

This particular image seems to have been heavily, heavily inspired by a 1975 photograph on this webpage (second from the top):

http://web.archive.org/web/20150602061844/http://d51791.com/pg22gohati.html